While Mayor Rob Ford was meeting with meeting Toronto Community Housing residents in Etobicoke on Friday, Deputy Mayor Norm Kelly convened a meeting of business leaders to discuss one of the most pressing issues on the city’s agenda: what to do with the Gardiner Expressway. He did not invite the mayor.

And so continues Toronto’s dual mayor system, one that has seen them bicker over everything. Mr. Ford and Mr. Kelly first dueled in December, over who was more responsive to the mass power outage after the ice storm. Mr. Ford wants to take down the Pride flag from city hall; Mr. Kelly wears a rainbow pin to show his support for lesbians and gays. A dispute broke out over who first suggested raising Ukraine’s flag at city hall. Both appeared to be in a race to keep outdoor skating rinks open through March Break. Mr. Kelly meets with Premier Kathleen Wynne; Mr. Ford says she should meet him instead. And on and on, with no end in sight.

So who is in charge? And can the business of the city really get done under this strange system?

In November, after the mayor admitted he had smoked crack, city council gave most of the mayor’s staff, budget and office space to Mr. Kelly. It is an unprecedented experiment. Councillor Josh Matlow is pleasantly surprised by the result.

“Council didn’t pick who the deputy mayor would be. Ironically, it was Rob Ford himself,” Mr. Matlow says. “Norm has exceeded all of my expectations. He has grown as a politician and as a person.”

Soon after Mr. Kelly got his new powers, “I remember I was sitting in a committee,” Mr. Matlow recalls. “Norm came into the room and gave everybody a kind of football punch on the shoulder. He was saying, ‘Go team go,’ and did that to people on the left, centre and right of the spectrum. I thought, ‘That’s refreshing.’ ”

Mr. Kelly now has 14 employees. This week he put them to work, inviting powerful advocates from the CAA, the Canadian Association of Movers, the Ontario Food Terminal Board, Redpath Sugar and the Retail Council of Canada, among others, to speak about a city staff report that recommends tearing down the Gardiner Expressway.

Designed to show Mr. Kelly’s clout, the event instead suggested a certain shakiness and inexperience.

On Thursday Mr. Kelly invited all councillors to the roundtable. Later his assistant, Isaac Ransom, sent out a statement, “to clarify and apologize,” saying only Councillors Michael Thompson and Denzil Minnan-Wong could attend.

This left the thorny question of Mr. Ford himself. Mr. Kelly did not invite him, and tried to keep the event under wraps until the last moment, fearing Mr. Ford’s reaction.

Mercifully, on Friday the mayor stayed in Etobicoke, sending Christine Maydossian, his policy advisor, to the gridlock roundtable. Around 11 a.m., Amin Massoudi, the mayor’s press attaché, texted the National Post to say, “Our office staff member was just asked to leave the deputy mayor’s ‘open’ round table event. She was there to observe only.”

Ms. Maydossian declined to comment. Mr. Kelly told reporters he did not know she had been removed. Earl Provost, the deputy mayor’s chief of staff, later sought to downplay her ejection.

“It was a misunderstanding,” he said. “Mistakes happen. This isn’t an exact science. It won’t be repeated.”

Still, several participants offered kind words to Mr. Kelly.

“I think that he did a very good job,” said Ms. Fletcher. “He really showed today he’s taken an initiative, to bring together a number of players.”

David Gerofsky, chief executive of First Gulf, the real estate firm that has bought the Unilever site at the foot of the Don Valley Parkway, wants the Gardiner gone. He praised Mr. Kelly’s office for the event.

“I was told that Rob Ford’s office wanted him to do this for the past two years,” Mr. Gerofsky said. “I am quite apolitical about who invited me. I am honoured to attend. It’s the good start of a conversation.”

Though stripped of many powers, Mr. Ford remains the city’s representative to the rest of the world. On Wednesday the mayor traveled to Ottawa to attend a meeting of the Federation of Canadian Municipalities — with mixed results.

Mayors from Montreal and Quebec City refused to shake Mr. Ford’s hand, calling him a distraction. Still, Mr. Ford clearly stated his goals: he wants federal cash to help build Toronto transit, and seeks to maintain Canada Post’s home delivery of the mail.

Outside the cozy confines of city hall Mr. Kelly sounded less coherent. Monday he stood beside Premier Kathleen Wynne in the Government Caucus Room at Queen’s Park. (Ms. Wynne, who can’t contain her contempt for Mayor Ford, has insisted since November to meet only with Mr. Kelly.)

Asked why he’d come, Mr. Kelly spoke in almost comical generalities.

“The premier and I share a deep affection for the city of Toronto,” Mr. Kelly said. “There is remarkable potential for Toronto to blossom. We are going to see green sprouts very soon.”

Mr. Ford, meanwhile, looks like the uncle who overstayed his welcome and can’t be budged from the couch. He last looked mayoral in the aftermath of the ice storm, appearing to take charge with daily news conferences.

Mr. Kelly is quite a different animal: a trained historian, he speaks in long and sometimes complicated metaphors. On the plus side, his inclusive strategy has some at city hall singing his praises.

It is increasingly unlikely the two men can learn to work together and that’s unfortunate. The current tug-of-war ensures that neither will warrant their name on a major civic square.